Music in the Twentieth Century explored many types of dissonance:
A suspension technically takes place when a note from a previous chord is held over, and then resolves into the new chord.
A color tone is any type of non-chord tone added to create a dissonant effect.
A polychord is formed when two or more triads sound simultaneously.
Upper extension chords are made by continuing to stack thirds on top of a triad. These chords can reach up to a 13th above the root.
A tone cluster or "clusterchord" is made by playing a group of adjacent semitones simultaneously.